Another 200 were wounded in the blasts, which occurred almost simultaneously in a crowded area of a district that is associated with the Shi'ite Muslim group Hezbollah.
"In a security operation that pleases Allah, the soldiers of the Caliphate were able to park an explosive bike and blow it up in a crowd of infidels … in the southern Dahieh suburb of Beirut," the Islamic State said in a statement.
Iran-backed Hezbollah has sent members to Syria to fight alongside forces loyal to President Bashar Assad. The Sunni Islamic State opposes Assad.
The group said the first blast was caused by explosives planted on a motorbike, after which a suicide bomber set off an explosive belt.
— Haidar Sumeri (@IraqiSecurity) November 12, 2015
A third body reportedly was found at the scene with an explosive belt that had failed detonate. Lebanese security forces are looking for a fourth extremist who fled the scene after bombings.
The blasts struck a Shi'ite community center and a nearby bakery, security sources said. The blasts were also close to a Hezbollah-run hospital.